Starshot and the Gravitational Lens

byPaul GilsteronApril 25, 2016

Although the idea of a mission to the Sun’s gravitational lens has been in Claudio Maccone’s thinking for a long time, it has never been linked with the financial resources of a concept study like Breakthrough Starshot. The Italian physicist led a conference on mission concepts in the early 1990s and submitted a proposal for an ESA mission in 1993. What’s striking to me is that throughout that time, Maccone has explored aspects of the mission he calls FOCAL that at one point seemed far too futuristic for our era. Could we, for example, do SETI with a FOCAL mission? Could we use it to enhance communications with an interstellar probe?

The answer to both is yes, but the problem was pushing a spacecraft out to 550 AU in the first place, a challenge involving flight times of many decades. Then the Breakthrough Starshot initiative emerged and suddenly Maccone found himself in Palo Alto talking about a well-funded study, one that looked to FOCAL to support interstellar probes both in terms of defining their target and enabling their data return. FOCAL was a bit less theoretical, and all those papers over the years now had ramifications in an ongoing mission design.

Power of the Lens

Stanford’s Von Eshleman was probably the first to think about using the lensing properties of mass to do science at the lensing distance and beyond, though Frank Drake and others have pondered the possibilities of boosting reception at the hydrogen line (1420 MHz), the famous ‘waterhole’ for interstellar communications. But most readers will also be familiar with the astronomical studies that have been conducted using the lensing of distant objects. A galaxy located behind an intervening galaxy can reveal itself by the bending of its light, another way of saying that mass shapes spacetime — the light is still following the shortest possible route.

In a similar way, light from an object directly behind the Sun can be ‘bent’ by the Sun’s mass, converging at the gravitational focus some 550 AU out. This can lead to misconceptions, especially the idea that we have to get a spacecraft to a specific distance and then stop there to take advantage of the effect. Not so — there is no focal ‘point’ here but a focal line. As we move through and past 550 AU, we take advantage of the fact that the focal line extends to infinity. Coronal effects from the Sun are diminished as we continue to travel and we have the opportunity to make observations of the object on the other side of our star.

A working constellation of FOCAL spacecraft could be critical to the success of a fast flyby mission like Breakthrough Starshot. We want to know as much as possible about what is around Alpha Centauri before we send our first probes. An infrastructure that can push a small sail to 20 percent of lightspeed gets us to the gravitational lens within days. Each spacecraft it delivers can then makes continuous observations as it moves away from the Sun in the direction opposite the Alpha Centauri system.

Speaking before Maccone at the Breakthrough Discuss meeting, Slava Turyshev (Caltech) pointed out that the gain for optical radiation through a FOCAL mission is 1011, a gain that oscillates but increases as you go further from the lens. This gives us the opportunity to consider multi-pixel imaging of exoplanets before we ever send missions to them. Lou Friedman, whose sail experience at JPL involved a study of a possible sail mission to Halley’s Comet, spoke of a FOCAL mission as ‘an interstellar precursor for Starshot or other destinations beyond the Solar System. Right now we are brainstorming,” he added. “We are studying spacecraft requirements to fly within the ‘Einstein ring’ and do the necessary maneuvering.”

I mentioned Von Eshleman above — he was the first to suggest using the gravitational lens for communications purposes in a 1979 paper, and as Slava Turyshev noted, this was where the practical application of General Relativity for space missions was truly born. But it has been Claudio Maccone who developed these ideas in a series of recent papers, noting that laser communications are deeply compromised at interstellar distances because of pointing accuracy problems and the need for power levels far beyond what we might expect from a StarChip.

Building Bridges Between the Stars

Is the gravitational lens, then, what Maccone likes to call a ‘radio bridge’? Bit Error Rate (BER) charts the possibilities. It’s the number of erroneous bits received divided by the total number of bits transmitted. A probe in Alpha Centauri space trying to communicate with a NASA Deep Space Network antenna — using parameters Maccone developed for a mission payload much larger than Starshot — suffers a 50 percent probability of errors (see The Gravitational Lens and Communications). But a FOCAL probe exploiting the gravitational lens picks up the signal without error. In fact, we don’t start seeing errors until we’re fully nine light years out.

I don’t have Maccone’s slides from the Palo Alto presentation, but the figure below comes from one of his papers, and it illustrates the same point.

Image: The Bit Error Rate (BER) (upper, blue curve) tends immediately to the 50% value (BER = 0.5) even at moderate distances from the Sun (0 to 0.1 light years) for a 40 watt transmission from a DSN antenna that is a DIRECT transmission, i.e. without using the Sun’s Magnifying Lens. On the contrary (lower red curve) the BER keeps staying at zero value (perfect communications!) if the FOCAL space mission is made, so as the Sun’s magnifying action is made to work. Credit: Claudio Maccone.

But as Maccone told the crowd at Stanford, we do much better still if we set up a bridge with not one but two FOCAL missions. Put one at the gravitational lens of the Sun, the other at the lens of the other star. At this point, things get wild. The minimum transmitted power drops to less than 10-4 watts. You’re reading that right — one-tenth of a milliwatt is enough to create error-free communications between the Sun and Alpha Centauri through two FOCAL antennas. Maccone’s paper assumes two 12-meter FOCAL antennas. StarShot envisions using its somewhat smaller sail as the antenna, a goal given impetus by these numbers.

Now we can start thinking about a galactic communications network. If we can start building out these bridges, we may well be latecomers in the activity. Maccone puts it this way:

The galaxy is a bonanza of stars that can be used as gravitational lenses. There may be civilizations that discovered that fact long ago. Perhaps we are the newcomers. The conclusion is that more advanced civilizations than we might have established sets of radio bridges between stars, a network of radio bridges, a ‘galactic internet.’ If this is true, then the conclusion is that as long as humanity is not capable of reaching the minimal focal distance of our own star, we will remain cut off from rest of galaxy in the sense of SETI.

The conclusion for StarShot: The first FOCAL spacecraft is sent out beyond 550 AU to the region in the sky precisely opposite to Alpha Centauri. This craft acts as our relay satellite, enabling communications between the Earth and any probe reaching our nearest neighbor. The second FOCAL mission is now sent to Alpha Centauri to create the radio bridge. All exploratory missions to come then have robust communications without the need for huge power resources aboard the spacecraft. The gravitational focus is thus our first target.

As Blakesley Burkhart (Harvard-Smithsonian Center for Astrophysics) noted in a follow-up panel, a mission to the gravitational lens contradicts a lot of things astronomers have been taught since their earliest days; specifically, the first thing you learn to do with a telescope is not to point it toward the Sun. FOCAL demands that we do just that, but the rewards are immense, not just in terms of exoplanet imaging and telecommunications, but also in discoveries we can’t anticipate, perhaps involving the Cosmic Microwave Background, itself a wonderful FOCAL target because being isotropic, it removes the need for exquisitely precise targeting.

A Voyager-class spacecraft, said Cornell University’s Zac Manchester, would take 150 years to reach 550 AU, while the Innovative Interstellar Explorer concept, developed in 2003, would reach the gravitational focus in about fifty years, using multiple Jupiter flybys. StarShot’s goal is to move fast enough to reach the lensing area in just a couple of weeks. Manchester noted the need for multiple spacecraft to sample the huge lensed image pixel by pixel. Think in terms of a spacecraft ‘array’ more than one or two craft. Just how we do this in the StarShot framework is something that research teams will be studying for some time to come, given the gradual realization that if you want to do interstellar, you’d better look at FOCAL first.

We’ll also have to take into account Geoffrey Landis’ findings in a paper just now becoming available on the arXiv site. It’s “Mission to the Gravitational Focus of the Sun: A Critical Analysis” (preprint), which looks at problems at realizing the FOCAL concept and in particular at acquiring a workable image. Claudio Maccone’s paper on radio bridges is “Interstellar Radio Links Enhanced by Exploiting the Sun as a Gravitational Lens,” Acta Astronautica Vol. 68, Issues 1-2 (January-February 2011), pp. 76-84 (abstract).

Comments on this entry are closed.

Marshall EubanksApril 25, 2016, 12:32

I think that the FOCAL communication has to be in the optical (or IR), not in the radio. A “near lens” – i.e., a star you are using as a gravitational lens from near the point of the first focusing as a lens – will put the raypaths quite close to the star’s surface (if you are at the focal distance, the raypaths will skim that surface). We know a lot about the dispersion caused by coronal plasmas in near Sun raypaths; these are very destructive to signal coherence. This can be solved by going to the IR or visible light wavelengths, where there is no dispersion due to stellar plasmas. (This is why spacecraft don’t communicate with the DSN near superior conjunction, i..e, when raypaths go near the Sun.) The stellar light will be a problem in the visible, but that can be solved by going in the IR (where stars are not as bright) and / or by using lasers turned to a deep stellar absorption band.

We do this with astronomical observations even now, though using the far larger gravitational wells created by entire galaxies or even clusters. At the level of the average single star, the distance is great enough to make acquiring the highly attenuated data all but impossible even if we are on the focal line.

Cheers, Paul, and of course we’re used to gravitational lensing on a galactic scale, but this still sounds as if every star (and other body as I look forward to reading tomorrow!) is a lens and we’re always on the focal line pointing somewhere because they’re spherical objects, so in practice that line doesn’t go to infinity because the data is attenuated.

And of course it’s fascinating that we might have to consider relativistic effects for the probes we send there. And as has also been said, the Fermi paradox implications are massive.

Correct, every star is a gravitational lens, but the amplification decreases with the square root of distance, while the field of view decreases with distance squared. So if you’re looking at the lens of a far-away star, it gives you trivial magnification of a randomly-picked vanishingly small portion of the sky.

Thanks Paul, this is the article I was waiting for. This is totally awesome.

Re “An infrastructure that can push a small sail to 20 percent of lightspeed gets us to the gravitational lens within days. Each spacecraft it delivers can then makes continuous observations as it moves away from the Sun in the direction opposite the Alpha Centauri system. ”

So, if I understand well, we are not talking (only) of FOCAL missions done with other technologies, but (also) of FOCAL missions done with Starshot technologies (StarChip, microsail, beamer). Correct? Is there a green light for a feasibility study?

Re “the need for power levels far beyond what we might expect from a StarChip.”

Are possible solutions being discussed? Also, has anyone worked out how the gravitational lens reception and transmission work when the antenna is moving at relativistic speeds?

If I understand this correctly, all those papers about the optimal way for ETs to communicate using powerful transmitters might just be wrong, because tiny transmitters might suffice? It does presuppose that there are very many transmitters, each targeted at a star. Perhaps this is also the place to start looking for alien transceivers in our own solar system, although the volume of space to search is mind bogglingly huge. What better way to stay hidden?

I wonder… imagine if ET has already put a set of devices around Sol, as a node in a communications network, each device being along a line opposite Sol from a nearby star. To route a signal, they would have to transmit it onward between themselves, i.e. a signal arrives from Alpha Centauri with a note to relay it on to Wolf 359; the device that receives it would then transmit on to the corresponding device in position opposite Wolf 359, which would basically be a chord across a circle of radius 550au or more. If the devices were transmitting with regular microwave aerials, perhaps we might be able to pick up a sidelobe transmission? Just a thought.

Geoffrey Landis’ paper is a pretty serious challenge to the FOCAL concept.

Key quote: “Thus, if we define the FWHM focal blur as the circle inside which half the light originates, the focal blur is exactly half the diameter of the planet, regardless of the size of the planet. Correcting the focal blur could be done if the telescope at the focus was able to resolve the width of the Einstein ring. But because of the radial demagnification of the gravitational lens, the width of the Einstein ring is half the angular width of the planet, and hence any telescope that could resolve the width of the Einstein ring could image the planet directly, without need for the gravitational lens.”

My understanding (repeated re-reading required) is that while the sun’s gravitational focus may give a large amplification in light gathering, it does not (on rather fundamental grounds) translate into greater resolving ability.

What Landis calls focal blur has also been called the unfavorable point spread function (PSF) of a gravitational lens. It can be addressed by computational deconvolution when the brightness of the Einstein ring is resolved around its perimeter. Figure 9 in Landis’ paper shows this clearly, although he does not mention that this would be useful for deconvolution, strangely.

The brightness ratio between the Einstein Ring and the corona could be a bigger problem. Landis explains this, but, strangely, does not carry it through to actually saying whether it is or is not a problem. He says “We want the signal to be greater than the noise”, but then does not follow through and do the comparison for his concrete example.

I generalized the classic “where are they?” to include both a physical presence “here”, and a sensed presence from somewhere “out there.”

In the Wikipedia article on Fermi’s Paradox you will note several solutions having to do with communication rather than transportation such as “Humans are not listening properly”; “Civilizations broadcast detectable radio signals only for a brief period of time”, and “Everyone is listening, no one is transmitting”.

So while ET may be somewhere (even right here!), we have not figured out how to sense them because, as many others have suggested, they may be using exotic means of communication which alleviates the need to travel. I think an Interstellar Network of Gravitationally Focused Communication rates as exotic. INGFoC – Lousy acronym!

Scott… beautifully put and very poetic. To think we’ve possibly been “shut out of SETI because we’ve yet to get to 550 AU”… sobering thought (I have a vastly overpowered 5mW laser-pointer laying around I could donate, ha ha)

I get the, uh, points that: (a) the gravitational focus is a focal line rather than a focal point and; (b) the FOCAL craft therefore doesn’t need to decelerate after reaching the focus in order to capture imaging or messaging from the target star.

Indeed, as today’s article points out, reception from the target star may get better as the craft goes further on out the focal line from 550 AU or so.

My question, though, concerns the fact that the FOCAL craft still is receding from us at quite a clip. My (hopefully approximately correct) back-of-the-envelope math reflects that it will take about three days (approximately 76.23684197039167 hours) at light speed for the telemetry from the FOCAL craft to reach us back here on Earth once it reaches 550 AU. If it gets to 550 AU in a couple of weeks, then every couple of weeks, it then will take another three days longer for the telemetry to reach us.

At what point does the distance to the FOCAL probe itself become an operational issue due to an increased error rate and/or overly long delays in receipt of telemetry?

I guess the simple solution would be to just send another FOCAL craft out — assuming that most of the cost of this approach is in the beamer infrastructure rather than in operationally sending the probes themselves.

However, as an alternative – if it indeed proved to be the case that the distance to a receding .20 c speed FOCAL craft ultimately presented a significant operational issue – one also perhaps just could send the FOCAL craft out at a slower speed.

There perhaps might be a sweet spot where the FOCAL mission reached a prime operational distance within a reasonable time but once there then was not traveling at such a speed that long distance communication with the probe itself became an issue unreasonably quickly.

(Well, I guess we could send the first out at .20 c for proof of concept both of the propulsion method and the efficacy of the gravitational lens in this context. Kind of hard to wait patiently on the first one if you know you can get there faster.)

If this concern is addressed in the underlying technical papers, my apologies. But as a layman, it is my initial question upon seeing that instead of centuries, decades, or even years, we now are actively contemplating getting to the gravitational focus in only a matter of days or weeks.

What a game changer. I had hoped that we would pursue a FOCAL mission in my lifetime, but the prospects had not been looking all that promising for it to actually come to pass. Now it looks like we may well be running multiple such missions toward multiple targets as a matter of course in the not too distant future.

“At what point does the distance to the FOCAL probe itself become an operational issue due to an increased error rate and/or overly long delays in receipt of telemetry?”

are the kind of thing we will need to find out, and bear in mind that many issues are still in play — see the Geoff Landis paper I referred to at the end of today’s post for a look at how difficult it will be to resolve an image. If I can get Claudio’s comments on your questions, I will, though he’s traveling and hard to reach right now. But like Lou Friedman said, “we’re brainstorming.” The FOCAL concept is going to get a very hard look using Breakthrough’s research dollars. Let’s hope it doesn’t turn out to be a showstopper for data return.

Even though image resolution may be an open issue, the drastic reduction in spacechip transmit requirements seems pretty solid. That being so, and bearing in mind that Starshot is a fly-through type mission with an acquisition time at target on order no more than an hour or so at 0.2 c, then we can arrange a FOCAL mission to arrive at the focal line at high speed. We will only be needing it for the short time that data is returning from Alpha Centauri. So it is no big deal that the FOCAL gravscope is receding so fast.

If we coat the one side of the sail with radioactive alpha emitters we could use the sail in a fission fagmentation configuration to accelerate or slow down, it could also act as a battery. Coating could be achieved by spraying an ionised radioactive material via a particle accelerator after photonic acceleration has been completed.

I would be careful about making such predictions. This concept has huge technical challenges, it might prove unfeasible yet. Remember that this 100 million is for research, not actual probes. I am interested in energy cost for lasers pushing this sail to 20% of light speed. Did anyone calculated how much ot would be?
I am much in favor of such mission, especially in view of FOCAL observations, but it is good to remain cold headed.

I would expect that the first FOCAL mission will be launched shortly after it becomes feasible to send it at a speed where it takes a few years to go there. Simply because it is unlikely that technology will develop from there to 0.2 c within just a few years. You did not think that the first operational beamer would right away provide the 0.2 c, did you?

If this is so, the probe receding along the line of focus will be much less of a problem.

As you and others say, sending and receiving data between Earth and the focal relay, while not as daunting as directly to AC, is still a huge problem. Solving it may require the focal relay to be much larger than the AC probe, and unable to be launched at 0.2 c ever.

It feels a bit like a second Renaissance. The implications are impressive.

I would love to know if there’s a way to synthesise data from the Einstein ring without going all the way out to the focal line. Can we do this within the inner solar system using accurate navigation, perhaps taking a cue from eLISA-style navigational accuracy?

Of course the data can be simulated, in-silico. The real thing, though, is only available out beyond 550 AU, and the first test mission will be quite risky.

The navigation precision that is required is on the order of meters, I think. Locating both the probe and the relay to the required precision on opposite sides of the sun would be very difficult. It would require a telescope with an aperture comparable to the solar lens. Perhaps a long baseline interferometer in solar orbit, or a sort of a solar system wide precision GPS with signals strong enough to reach out beyond 550 AU. Once the probe gets out of range of that GPS (and it will, or else we would not need the focal relay in the first place), the only way to keep communications going is to “autofocus”, i.e. monitor the link, detect sideways drift, and maneuver the relay to compensate before the signal becomes undetectable. If you lose communications at any time, it will be lost for good and you can write the probe off. Each probe would need its own relay, of course.

Not a stupid question at all, DJ. And the answer is yes — every massive body produces a lens like this. More on this tomorrow, when I’ll talk about ideas on using planet-sized objects to take advantage of gravitational lensing.

You might want to see this presentation by Dr. Slava Turyshev at the Keck Institute for Space Studies Workshop on Exploring the Interstellar Medium. Slava and I are proposing to study use of the solar gravity lens focus for very high resolution imaging a potentially habitable exo-planet: ihttps://www.youtube.com/watch?v=eEZ6zYZ6lDQ

Sending Starchips to the Sun’s gravitational lens for Alpha or Proxima Centauri will likely require a beamer in the Northern Hemisphere (maybe Arizona). Using a beamer in the Atacama Desert (23-24 degrees South) to reach 60-62 degrees North would not be an option.
A Northern Hemisphere beamer could be a “test” installation for the full StarShot. This could be a 1/100th to 1/10th scale and still be viable for sending Starchips past 550AU in less than a year. Aiming for 0.02 c would give an intermediate goal an order of magnitude easier than 0.2 c and would be a great test of all the technologies.
We waited 9 1/2 years for New Horizon’s – waiting one year after launch for a focal mission looks pretty good.

Once (or a more skeptical If) we learn to digitize consciousness and move it from biological brains to digital storage and back, the galactic communications network will become a galactic transportation network.

I’ve wondered about the assertion that the “line” projects from an endpoint, moving radially from the star to – where? Surely there’s some sort of curve that relates on one axis distance from the star and on the other resolution or magnification or something?

On the issue of achieving 550AU in a few weeks (I can hardly believe I typed those words!): how would the device actually stop? Or does it start to beam back data once at 550AU, and thence, out to some point, as I asked above?

The very notion of two 12 meter class antennas whispering across the abyss is simply startling.

Landis’ critique is well written, understandable even to a layperson, and should be part of any discussion of gravitational lens imaging discussions. Before reading the paper, I was also wondering about the imaging, and this paper clarifies and explains the issues nicely. Figure 2 is particularly relevant, IMO.

I think there is at least one way to overcome the blurriness issue which may overcome this problem, making the approach attractive for imaging. But as Landis’ asks, for the increased resolution, is the cost and difficulty worth it compared to other approaches?

I think the one most critical question is whether the weak light of a planet is drowned out by the coronal background at the distance of the Einstein Ring. Landis properly poses this question when he says “We want the signal to be greater than the noise”, but as far as I can tell he stops short of answering it.
It is not clear to me why, all the data seems to be there. Did I miss something? Perhaps an exercise left to the reader. I wish I had more time ….

If planets are not bright enough to observe, we will have to make do with the surfaces of stars and supermassive black holes, I am afraid.

It would be fine business to test this gravscope comms paradigm. Let’s imagine we wish to locate and test transceivers on opposite sides of old Sol, communicating via grav lensing at very low power. They are each going to have to be critically further out than 550 AU because of the proximity divergence. There might be enough info in the Landis paper to calculate this minimum focal distance, but I feel as if I haven’t had enough coffee; so perhaps someone has a ready answer at hand to save skull sweat?

Although a splendid proof of principle that SpaceChip comms may be done on a shoestring, there are other issues. We can’t place both transceivers from the same location of Earth’s orbit, and indeed we have to wait 6 months between launches to get them diametrically opposed.

This seems to be a key experiment to spot any potential problems and to establish a firm comms stepping stone for the StarShot mission.

Thank you Louis Friedman for the video. It highlights the painstakingly precise navigation required for any gravscope transceiver. A movement of a mere 10 metres across the image plane drops you 10 dB!! By any reckoning, 10 metre accuracy over almost 1,000 AU is – uh – demanding.

If the probe isn’t sent out on an exact Sol radius, it will begin to curl back in after a while, and long before its endpoint is reached. Thus it’s going to need active navigation. How much I do not presently know: are onboard lasers going to suffice? And how is a successful comms test communicated back from such a tiny device?

We must also take into consideration that the planets especially Jupiter cause the sun to wobble due to centre of mass effect which could make things even more complicated. We would need to cancel this effect out somehow or risk degradation of the image.

I think it is exactly a factor of two, isn’t it? I seem to remember that from studying geometrical optics. So in order to get two relays to be in each other’s focus, you need to send them out 1100 AU, each.

Since the beam produced by an axicon (or equivalent optical element) is a thin ring of effectively constant thickness relative to the ring’s overall diameter, a significant fraction of its total energy would pass by not just one, but both stars in a gravitational lens system. Of course, the spreading angle of the “hollow beam” is very small, and very high quality “optics” would be required at transmission. Unless you are very close to the focal point beyond the second lens of such a system, the beam energy is very diffuse. If azimuthal modulation is incorporated in the ring’s energy, interception of a fragment would hinder any attempt to recover and demodulate the complete signal as transmitted.

Re “To ensure that the Einstein ring is larger than the corona and not obscured by it, the mission would have to sit even further, at a distance of more than 2,000 AU, says Landis. That’s much further than the 550 AU that previous analyses have suggested.”

So what? Two months instead of two weeks for a Starshot nanoprobe, no big deal.

Is the summary complete and accurate? (I haven’t read the full Landis paper yet).

If each sail weights around 4 grams then 20 to 50 grams of alpha emitters should stop the the 0.2 c sail. That is a very small amount of material, which could be used to manuvour the sail and keep it on target as well. Using these sails could be just what is needed to send GW detectors along the focus line which for GW’s is all the way out. Could be used to probe neutron and black hole orbital dynamics to high precision. GW detectors can be made very small.

One figure of merit for a braking technology is specific force per unit mass of that tech (N/Kg), since, together with payload mass, this determines the deceleration obtained. We can have onboard lasers with force P/c that are simply turned on and off. The weight of their power supply, if used for no other purpose, must also be included. Then there’s this radioactive idea. I have no idea if they compare with an onboard laser. Certainly they continuously radiate isotropically by default, but can provide directed thrust when seated at the focus of a paraboloid. The weight of the paraboloid must also be included, and the mechanism to change to directed thrust mode surely also has some mass?

You must have made a mistake, Michael. An alpha emitter could not even stop itself. Far from it. Not even if all of its atoms emitted their alpha particles into the same direction at the same time. The alpha particle itself only goes 5% of c, and the nucleus would be decelerated only a small fraction of that.

In Centauri Dreams, Paul Gilster looks at peer-reviewed research on deep space exploration, with an eye toward interstellar possibilities. For the last twelve years, this site coordinated its efforts with the Tau Zero Foundation. It now serves as an independent forum for deep space news and ideas. In the logo above, the leftmost star is Alpha Centauri, a triple system closer than any other star, and a primary target for early interstellar probes. To its right is Beta Centauri (not a part of the Alpha Centauri system), with Beta, Gamma, Delta and Epsilon Crucis, stars in the Southern Cross, visible at the far right (image: Marco Lorenzi).

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